Hagen von Eitzen
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397/400 score
 Jan 17 comment Questions about decimal expansion being able to represent all real numbers Where's that WP article? Regular languages over finite alphabets are countable. - And the questions are full of non sequiturs, I'm afraid. - There are simple proofs that decimal expansions exist. no matter which of several definitions of "real number" to start from, probably also in your "several books". Jan 16 comment Cardinality of set of all bijections $\mathbb{N}\to\mathbb{N}$; is my proof correct? I assume $F(f)(x)=2x+f(x)$? Jan 16 comment Are there infinitely many pairs of primes where one divides one more than the square of the other? Another pair: $p=52989271100609562179203955678778467019711275902953450662090516283476995513442‌​4689676262369$, $q=13872771278047838271141861031862463922584503581717836900799180321360252259546‌​02593712568353$ - in my suggestion to look for $F_{n-1},F_{n+1}$, it is necessary (but not sufficient) that $n-1, n+1$ are twin primes. Jan 16 comment Are there infinitely many pairs of primes where one divides one more than the square of the other? All your examples are of the form $F_{n-1}, F_{n+1}$ with $F_n$ denoting the $n$th Fibonacci numbre Jan 16 answered How to aproach that this equation has infinite positive solutions? Jan 16 comment Primes as sum of squares. Your strategy is doomed to fail. After all, $p_j$ can always be written as sum of four squares, so this can hardly lead to a contradiction. Jan 16 answered Is $\cos(1)^2$ irrational? Jan 16 answered Does this graph contain $K_5$ or $K_{3,3}$ as subdivision or minor? Jan 16 comment Why probability of intersection of independent events cannot be attained by multiplying Given that 24/100 is not 20/100, how dare you assume that the events are independent? Jan 16 comment Limits of floor functions What are your thought? What are the values of $f(0.0001)$, $f(-0.0001)$, $f(0)$, $f(-0)$? Jan 16 comment Proof that $f:\mathbb R\to[-1,1], f(x)=\cos x$ is surjective Do you know that the cosine function is continuous? And which definition of cosine do you work with (geometric, power series, from complex exponential, ...)? Jan 16 answered Prove that if $f$ is convex and upper bounded, it must be constant. Jan 16 answered How to calculate what percentage a fraction is Jan 15 answered can a number of the form $x^2 + 1$ be a square number? Jan 15 comment Algorithm for finding “fact families” From the text I learn: A "multiplication fact" is one member of a "fact family" (and there may be several multiplication facts in a fact family) and $2\times 3=6$ is a fact family. Also, fact families have several "dividends". - This is totally weird. My best bet would be that a fact family is a collection of related facts, such as $a\cdot b=c$, $b\cdot a=c$, $c:a=b$, and $c:b=a$. That interpretation matches some of the information readable from the problem statement, but it clearly contradicts others. Jan 15 comment How to prove that $f=id_A$? @bolzanoman There are so few steps that it is hard to see what is meant with final step.- Given $x\in A$, we want to show that $f(x)=x$. By surjectivity of $f$, there exists $y$ with $x=f(y)$. Then by this and the property of $f$, we have $f(x)=f(f(y))=(f\circ f)(y)=f(y)=x$ as desired. Jan 15 answered Sum involving the “distance to the nearest integer function” Jan 15 comment Showing that the mapping $a\in M, a^3=1,x\mapsto ax^2a^2$ is an automorphism of $M$ As stated, the problem statement is wrong. It has already been noted that $M$ needs to be commutative. Moreover, $f$ may fail to be onto: Let $(M,\cdot)=(\mathbb N_0,+)$ and $a=0$. Then $f(x)$ is even for all $x$. Jan 15 answered Nullary Arithmetic Product (at Wiki) Jan 15 comment $e^{\pi\sqrt N}$ is very close to an integer for some smallish $N$s. What about $\pi^{e\sqrt N}$? Instead of the last sentence I'd remark that $\pi^x$ is extremely dull and unnatural compared to $e^x$.